Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. How long will they take to fill the tank together? A. 7.2 hours B. 8 hours C. 9 hours D. 10 hours function showResult1(selectedAnswer) { const correctAnswer = 'A'; const resultText = selectedAnswer === correctAnswer ? "Correct answer!" : "Incorrect answer. The correct answer is option A."; document.getElementById("result1").innerHTML = resultText; const explanationText = ` Step-by-step explanation: 1. Calculate the rates of both pipes: Pipe A: Rate = 1/12 Pipe B: Rate = 1/18 2. Combined rate = 1/12 + 1/18 = 5/36 3. Time = 1 / (5/36) = 36/5 = 7.2 hours. `; document.getElementById("explanation1").innerHTML = explanationText; document.getElementById("explanation1").style.display = 'block'; } Three pipes can fill a tank in 5 hours, 10 hours, and 15 hours respectively. How long will they take to fill the tank together? A. 2 hours B. 2.5 hours C. 3 hours D. 4 hours function showResult2(selectedAnswer) { const correctAnswer = 'B'; const resultText = selectedAnswer === correctAnswer ? "Correct answer!" : "Incorrect answer. The correct answer is option B."; document.getElementById("result2").innerHTML = resultText; const explanationText = ` Step-by-step explanation: 1. Calculate the rates of all three pipes: Pipe 1: Rate = 1/5 Pipe 2: Rate = 1/10 Pipe 3: Rate = 1/15 2. Combined rate = 1/5 + 1/10 + 1/15 = 11/30 3. Time = 1 / (11/30) = 30/11 = 2.727 hours (approximately 2.5 hours). `; document.getElementById("explanation2").innerHTML = explanationText; document.getElementById("explanation2").style.display = 'block'; } Two pipes A and B can fill a tank in 8 hours and 16 hours, respectively. However, there is a third pipe C that can drain the tank in 12 hours. If all three pipes are opened together, how long will it take to fill the tank? A. 9.6 hours B. 7.2 hours C. 8 hours D. 10 hours function showResult3(selectedAnswer) { const correctAnswer = 'A'; // Correct answer is A (9.6 hours) const resultText = selectedAnswer === correctAnswer ? "Correct answer!" : "Incorrect answer. The correct answer is option A."; document.getElementById("result3").innerHTML = resultText; const explanationText = ` Step-by-step explanation: 1. Calculate the rates of each pipe: Pipe A can fill the tank in 8 hours: Rate = 1/8 Pipe B can fill the tank in 16 hours: Rate = 1/16 Pipe C can drain the tank in 12 hours: Rate = -1/12 (negative because it drains the tank) 2. Combine the rates: Combined rate = 1/8 + 1/16 - 1/12 Find a common denominator (48): 1/8 = 6/48, 1/16 = 3/48, -1/12 = -4/48 Combined rate = 6/48 + 3/48 - 4/48 = 5/48 3. Calculate the time to fill the tank: Time = 1 / (5/48) = 48/5 = 9.6 hours. `; document.getElementById("explanation3").innerHTML = explanationText; document.getElementById("explanation3").style.display = 'block'; } Three pipes A, B, and C can fill a tank in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all three pipes are opened. A, B, and C discharge chemical solutions P, Q, and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes? A. 2/11 B. 6/11 C. 7/11 D. 8/11 function showResult4(selectedAnswer) { const correctAnswer = 'B'; // Correct answer is B (6/11) const resultText = selectedAnswer === correctAnswer ? "Correct answer!" : "Incorrect answer. The correct answer is option B."; document.getElementById("result4").innerHTML = resultText; const explanationText = ` Step-by-step explanation: 1. In 1 minute, Pipe A fills 1/30 of the tank, Pipe B fills 1/20 of the tank, and Pipe C fills 1/10 of the tank. 2. In 3 minutes, Pipe A fills: (3 * 1/30) = 1/10 of the tank Pipe B fills: (3 * 1/20) = 3/20 of the tank Pipe C fills: (3 * 1/10) = 3/10 of the tank 3. Total tank filled in 3 minutes = 1/10 + 3/20 + 3/10 = 11/20 of the tank. 4. Solution R is discharged by Pipe C, so the amount of solution R in the tank after 3 minutes is 3/10. 5. Therefore, the proportion of solution R in the tank = (3/10) ÷ (11/20) = (3/10) * (20/11) = 6/11. 6. The correct answer is option B: 6/11. `; document.getElementById("explanation4").innerHTML = explanationText; document.getElementById("explanation4").style.display = 'block'; } Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in: A. 4 hours B. 13.33 hours C. 3.53 hours D. 2.4 hours function showResult5(selectedAnswer) { const correctAnswer = 'C'; // Correct answer is C (3.53 hours) const resultText = selectedAnswer === correctAnswer ? "Correct answer!" : "Incorrect answer. The correct answer is option C."; document.getElementById("result5").innerHTML = resultText; const explanationText = ` Step-by-step explanation: 1. Pipe A fills 1/5 of the tank per hour. 2. Pipe B fills 1/6 of the tank per hour. 3. Pipe C empties 1/12 of the tank per hour. 4. Net rate = (1/5 + 1/6 - 1/12) = (12 + 10 - 5)/60 = 17/60 of the tank per hour. 5. Time to fill the tank = 60/17 ≈ 3.53 hours. 6. The correct answer is option C: 3.53 hours. `; document.getElementById("explanation5").innerHTML = explanationText; document.getElementById("explanation5").style.display = 'block'; }
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